Convergence Order of a Finite Volume Scheme for the Time-Fractional Diffusion Equation

DOI10.1007/978-3-319-57099-0_4zbMath1371.65090OpenAlexW2605920586MaRDI QIDQ5274926

Jürgen Fuhrmann, Abdallah Bradji

Publication date: 7 July 2017

Published in: Lecture Notes in Computer Science (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/978-3-319-57099-0_4

zbMATH Keywords

convergenceerror estimateimplicit schemefinite volume schemeCaputo derivativetime-fractional diffusion equationSUSHI schemediscrete gradientnon-conforming grid

Mathematics Subject Classification ID

Initial-boundary value problems for second-order parabolic equations (35K20) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) Error bounds for initial value and initial-boundary value problems involving PDEs (65M15) Mesh generation, refinement, and adaptive methods for the numerical solution of initial value and initial-boundary value problems involving PDEs (65M50) Fractional partial differential equations (35R11) Finite volume methods for initial value and initial-boundary value problems involving PDEs (65M08)

Related Items (5)

Convergence analysis of a finite volume scheme for a distributed order diffusion equation ⋮ SUSHI for a non-linear time fractional diffusion equation with a time independent delay ⋮ A New Optimal $$L^{\infty }(H^1)$$–Error Estimate of a SUSHI Scheme for the Time Fractional Diffusion Equation ⋮ Notes on the convergence order of gradient schemes for time fractional differential equations ⋮ A new analysis for the convergence of the gradient discretization method for multidimensional time fractional diffusion and diffusion-wave equations

Cites Work

• Unnamed Item
• Fractional derivatives for physicists and engineers. Volume I: Background and theory. Volume II: Applications
• The Galerkin finite element method for a multi-term time-fractional diffusion equation
• Some abstract error estimates of a finite volume scheme for a nonstationary heat equation on general nonconforming multidimensional spatial meshes.
• A fully discrete difference scheme for a diffusion-wave system
• GRADIENT SCHEMES: A GENERIC FRAMEWORK FOR THE DISCRETISATION OF LINEAR, NONLINEAR AND NONLOCAL ELLIPTIC AND PARABOLIC EQUATIONS
• Boundary conforming Delaunay mesh generation
• Discretization of heterogeneous and anisotropic diffusion problems on general nonconforming meshes SUSHI: a scheme using stabilization and hybrid interfaces

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